In recent years near infrared (NIR) spectroscopy has been used as a means of indirectly determining several characteristics of petroleum products, and especially of fuels, including properties such as octane number, Reid vapor pressure, distillation points, and so forth. Using octane number as an example, its determination via NIR involves 1) measuring the NIR spectra of a set of dosely related fuels (a "calibration set") whose octane numbers have been independently determined using knock engines according to, e.g. ASTM methods 2699, 2700, and 2885, 2)developing a correlation between the NIR spectrum (i.e., absorption intensity as a function of wavelength over some wavelength range) of each member of the set and its corresponding octane number by some mathematical technique applied to the entire set (for example, multivariate analysis using principal component regression, partial least squares regression, factor analysis, multilinear regression, and so forth), and 3) applying the set of resulting correlation equations to an unknown sample of interest not in the calibration set to calculate the octane number of the sample from its measured NIR spectrum. It is clear from the foregoing that this method is a secondary method for determination of octane, as it depends on a primary standard of measurement as described in ASTM method 2699 and 2700.
The accuracy and scope of applicability of every secondary method of measurement is limited by the assumptions--whether explicit or implicit--incorporated into the relationship between the secondary and primary measurements. An important and vexing limitation on the nexus between the octane number of an unknown sample as calculated from its NIR spectrum, and the octane numbers as measured for the primary standards used for the calibration, is that the calibration set must bracket the region within which the sample lies. That is, if the members of the calibration set be viewed as independent vectors, then the sample must be at least closely approximated by a linear combination of these independent vectors. Another operational limitation which frequently applies is that the calibration set is not transferable from one refinery to another, that is, each refinery in using NIR to measure octane must develop its own calibration set. This is tantamount to saying that the octane number of any sample A will be poorly approximated by a linear combination of independent vectors (the calibration set) unless the independent vectors are obtained from the same set of samples from which A is obtained. The practical effects of these limitations are that a calibration set is best defined for each locale or refinery determining octane number by NIR, and that additional members must be added to the calibration set whenever the sample lies outside the "space" bounded by the calibration set.